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Gingerbreadman Map
In dynamical systems theory, the Gingerbreadman map is a chaos theory, chaotic two-dimensional map. It is given by the Piecewise linear function, piecewise linear transformation:. See in particular Fig. 3.3. : \begin x_ = 1 - y_n + , x_n, \\ y_ = x_n \end See also * List of chaotic maps References External links * Chaotic maps Exactly solvable models {{fractal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Dynamical Systems Theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations by nature of the ergodic theory, ergodicity of dynamic systems. When differential equations are employed, the theory is called continuous time, ''continuous dynamical systems''. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a Principle of least action, least action principle. When difference equations are employed, the theory is called discrete time, ''discrete dynamical systems''. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Chaos Theory
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas. Text was copied from this source, which is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Piecewise Linear Function
In mathematics, a piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. Definition A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".) If the domain of the function is compact, there needs to be a finite collection of such intervals; if the domain is not compact, it may either be required to be finite or to be locally finite in the reals. Examples The function defined by : f(x) = \begin -x - 3 & \textx \leq -3 \\ x + 3 & \text-3 < x < 0 \\ -2x + 3 & \text0 \leq x < 3 \\ 0.5x - 4.5 & \textx \geq 3 \end is piecewise linear with four pieces. The graph of this function is shown to the right. Since the graph of an affine(*) function is a [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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List Of Chaotic Maps
In mathematics, a chaotic map is a map (mathematics), map (an Discrete-time dynamical system, evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems. Chaotic maps and Iterated function, iterated functions often generate fractals. Some fractals are studied as objects themselves, as set (mathematics), sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems). List of chaotic maps List of fractals * Cantor set * de Rham curve * Gravity set, or Mitchell-Green gravity set * Julia set - derived from complex quadratic map * Koch snowflake - special case of de Rham curve * Lyapunov fractal * Mandelbrot set - derived from complex quadratic ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Chaotic Maps
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program aired on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids, Cartoon Network and Disney XD. It was brought over to the United States from Denmark by Bryan C. Gannon and Chaotic USA Entertainment Group, and produced by Chaotic USA Entertainment Group, 4Kids Productions and Bardel Entertainment. The trading card game came out 6 September 2006 in the U.S. and Canada. Each card comes with a unique code which the owner can upload onto the Chaotic website. This allows the owner to trade and play online using their own card collection. The game was well known to be the only game with a TV show, an online game, and a TCG that were all integrated. However, the online game is currently closed. The rights have since defaulted to Bryan C. Gannon, who's leading an effort to revive the game for modern audiences by licensing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |